Can you switch the type of WordPress site you have?

Generally self–hosted version of WordPress is not considered to have types. Other than multisite for hosting multiple sites on single WordPress installation.

From quick look you seem to have used hosted site from a company that built on top of WordPress.

To switch to a generic self–hosted WP installation you would need to:

  1. Acquire standard WP export file of your content or re–create the content on the new site.
  2. Come up with replacement functionality for whatever you were getting from the hosted platform.

Depending on exact platform moving away can range from trivial (wordpress com by Automattic will happily give you export file and often even exact theme you were using) to highly challenging (specialized platforms with complex proprietary functionality).